`hati.(hatjxxhatk)+hatj.(hatixxhatk)+hatk.(hatixxhatj)` is equal to

The value of the following expression hati.(hatjxxhatk)+j.(hatixxhatk)+hatk.(hatjxxhati) is

(a*hati)hati+(a*hatj)hatj+(a*hatk)hatk is equal to

[[hati, hatk, hatj]]+[[hatk, hatj, hati]]+[[hatj, hatk, hati]] is equal to

If a.hati=4 then (axx hatj).(2hatj-3hatk) is equal to

(a.hati)hati+(a.hatj)hatj+(a.hatk)hatk

a.hati=a.(2hati+hatj)=a.(hatj+hatj+3hatk)=1, then a is equal to

If d is the shortest distance between the lines vecr =(3hati +5hatj + 7hatk)+lambda (hati +2hatj +hatk) and vecr = (-hati -hatj-hatk)+mu(7hati-6hatj+hatk) then 125d^(2) is equal to ____________.